Adjust oven racks to the upper-middle and lower-middle positions. Preheat oven to 350 degrees. Line 2 baking sheets with parchment paper or silicone mats.
In a medium bowl or on to a piece of parchment paper, sift together flour, baking powder, baking soda, and salt. Set aside.
In an electric mixer fit with the paddle attachment, or with an electric mixer on high speed, cream butter until pale and fluffy. Add the granulated and brown sugars and beat until the mixture is smooth (not gritty when you rub between your thumb and finger).
Add egg and vanilla and beat on low speed until blended, scraping down the sides of the bowl as necessary.
Add the flour mixture in batches (about 1 cup at a time) and mix on low speed until just blended. Add the M&Ms and stir by hand until just combined. If you put the M&Ms in a standing mixer, even on low speed, they will get crushed and broken in the dough. (Optional: If it's hot in your kitchen, consider chilling the cookie dough for 20 minutes or so. If the dough is too soft, your cookies will spread too much. )
Working with 1 heaping tablespoon of dough at a time, roll dough into 1 1/2-inch balls and lay on prepared baking sheets about 2 inches apart. (I use the OXO medium cookie scoop, a size 40 portioner, and do 12 scoops of dough per baking sheet). If desired, press extra M&Ms into the outside of each dough ball.
Bake until the cookies are starting to brown around the edges, about 10 minutes. Remove baking sheets from oven and carefully drop (more like slam) baking sheets on counter to remove air bubbles from cookies.
Return to oven and bake 2 minutes longer. Remove from oven and cool on baking sheets for 2 minutes, then transfer to wire racks to cool completely.